Computed tomography (CT) provides a diagnostic and measuring method for medicine and test engineering with the aid of which internal structures of a patient or test object can be examined without needing in the process to carry out surgical operations on the patient or to damage the test object. In this case, there are recorded from various angles a number of projections of the object to be examined from which it is possible to calculate a 3D description of the object.
It is generally known to solve this problem by using the so called filtered projection (filter back projection FBP), the following documents being referenced by way of example [Bu04]: Buzug: “Einführung in die Computertomographie” [“Introduction to computed tomography”], 1st edition 2004, Springer-Verlag, ISBN 3-540-20808-9 and [KS84] Kak, Slaney: “Principles of Computerized Tomographic Imaging”, 1987, IEEE Press, ISBN 0-87942-198-3. FBP is a high performance computing method in which measured projections are filtered and back projected onto the image.
In this method, the image quality depends on the applied filters or convolution cores. These can be specified exactly in analytical terms for simple scanning geometries. Essentially, these are circular paths in the case of which many projections are recorded in uniform angular steps. More complex recording geometries that violate these assumptions lead to problems when attempting to determine the filters analytically. An example of this is tomosynthesis, where in the most general case only a few projections are obtained on a free path from a restricted angular distance.
Iterative methods such as the algebra reconstruction method (ART) have proved their worth for such reconstruction problems. Reference is made in this regard to the following documents [Bu04]: Buzug: “Einführung in die Computertomographie” [“Introduction to computed tomography”], 1st edition 2004, Springer-Verlag, ISBN 3-540-20808-9 and [KS84] Kak, Slaney: “Principles of Computerized Tomographic Imaging”, 1987, IEEE Press, ISBN 0-87942-198-3 and [WZM04] T. Wu, J. Zhang, R. Moore, E. Rafferty, D. Kopans, W. Meleis, D. Kaeli: “Digital Tomosynthesis Mammography Using a Parallel Maximum Likelihood Reconstruction Method”, Medical Imaging 2004: Physics of Medical Imaging, Proceedings of SPIE Vol., 5368 (2004) 1-11. It is advantageous in the case of this ART that iterative methods require no filters such as are necessary in the case of FBP. Because of their iterative nature, however, their computational period is substantially longer and is therefore often not feasible in practice. A further disadvantage of ART resides in the fact that by contrast with FPB this method cannot be used for any construction of subregions of the object (reasons of interest, ROI).
Reference is made by way of addition to patent application US 2005/0058240 A1, in which the inventor calculates reconstruction filters analytically by using very greatly simplifying, heuristic assumptions. The method is therefore limited to a few simple recording geometries and, moreover, to tomosynthesis.
The problem therefore exists of finding an efficient method for reconstruction of tomographic representations of an object from projection data that, on the one hand, does not place excessively high requirements on the computing power required for the reconstruction but, on the other hand, can also be used for any desired recording geometries and relative movements between radiation source, detector and object during the measurement.